A323979 Expansion of determinant of 120 X 120 matrix M_{u,v} = q^(maj(u*v^-1)) where u, v in S_5 and maj = MacMahon's major index (cf. A008302).
1, 0, -60, -80, 1680, 4704, -25660, -128640, 150420, 2062160, 2230548, -19194240, -63712740, 57664320, 724837020, 1055778256, -3865916310, -17164305600, -7987686380, 111558610080, 309981082824, -83708879920, -2310552888780, -4721178106560, 4129349973890, 39231750371520, 64807106219940, -86501225014320, -580167287063160, -840576756949440, 1330114847500228
Offset: 0
Links
- Jinyuan Wang, Table of n, a(n) for n = 0..1200
- C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411 (2005), 68-166; arXiv:math/0503507v2 [math.CO], 2005. See Theorem 56.
Formula
G.f.: (1-q^2)^60*(1-q^3)^80*(1-q^4)^90*(1-q^5)^96.